👉 The findings in this mathematical study reveal that the relationship between two variables, X and Y, is significantly non-linear, as evidenced by a quadratic trend in the scatter plot of their data. Specifically, the model indicates that Y increases at an accelerating rate with X, suggesting a quadratic function of the form Y = ax^2 + bx + c. The analysis also shows that the rate of this acceleration, or the second derivative of Y with respect to X, is positive, confirming that the relationship is indeed convex. Furthermore, the study found that the optimal value of X for maximizing Y is not at the vertex of the parabola but rather at a point where the derivative of the quadratic function equals zero, indicating a critical point that results in the highest value of Y. These findings have implications for understanding complex systems where growth or performance accelerates over time, such as in economics or population dynamics.
